Statistical-Theory Analysis of theMg24(n, p)Na24and theAl27(n, α)Na24Reactions

Previously reported measurements of the average cross sections for the ${\mathrm{Mg}}^{24}(n, p){\mathrm{Na}}^{24}$ and ${\mathrm{Al}}^{27}(n, \alpha ){\mathrm{Na}}^{24}$ reactions are compared with a detailed statistical-theory calculation in which information on the spin and parity of possible final states is included. The calculations employ nuclear transmission functions evaluated from an optical model of the nucleus. Good agreement is obtained between the calculated and measured average cross sections for neutron energies from the effective thresholds of the reactions to 10 MeV in the center-of-mass system. For a given value of the nuclear potential, the data yield a unique value for the effective radius of the nucleus with its associated particle, ($R_0+1.5d$), where $d$ is the surface-thickness parameter. In agreement with the formulation of Lang, a value of 3.6 for the level-density parameter $a$ for ${\mathrm{Al}}^{27}$ is obtained from a theoretical fit of ${\mathrm{Al}}^{27}(n, \alpha )$ cross-section results at the higher neutron energies. Fluctuations observed in the ${\mathrm{Mg}}^{24}(n, p){\mathrm{Na}}^{24}$ cross section are attributed either to the interference of overlapping levels in the compound nucleus ${\mathrm{Mg}}^{25}$, or to statistical variations in the number of levels of spin type ${\frac{9}{2}}^{-}$ and ${\frac{7}{2}}^{-}$ in the compound nucleus. These are the principal levels that give rise to the product, ${\mathrm{Na}}^{24}$.